{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QB7B2J47OIPGXH564HKNIS3NF3","short_pith_number":"pith:QB7B2J47","canonical_record":{"source":{"id":"1704.05616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-19T05:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"a3dbe345c27858ae1535df009dcc6d66c3178a21f17844c1f303a7f9e1e159c1","abstract_canon_sha256":"0f07532d5798250b55c56a1985fcfd519d743d47da7a7bde0fc79bca71bb43ff"},"schema_version":"1.0"},"canonical_sha256":"807e1d279f721e6b9fbee1d4d44b6d2ef5479b19d6a67ce802752dfba77cd2a4","source":{"kind":"arxiv","id":"1704.05616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05616","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05616v1","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05616","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"QB7B2J47OIPG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QB7B2J47OIPGXH56","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QB7B2J47","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QB7B2J47OIPGXH564HKNIS3NF3","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-19T05:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"a3dbe345c27858ae1535df009dcc6d66c3178a21f17844c1f303a7f9e1e159c1","abstract_canon_sha256":"0f07532d5798250b55c56a1985fcfd519d743d47da7a7bde0fc79bca71bb43ff"},"schema_version":"1.0"},"canonical_sha256":"807e1d279f721e6b9fbee1d4d44b6d2ef5479b19d6a67ce802752dfba77cd2a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:06.993810Z","signature_b64":"bicM/la4j+u+Lrc5rAeISlQx6wLCDuWdEpGjUQ/Vvc7bmd9LBclUMguoL22zAueQrFYDnhIgRVxu4DHhWcH4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"807e1d279f721e6b9fbee1d4d44b6d2ef5479b19d6a67ce802752dfba77cd2a4","last_reissued_at":"2026-05-18T00:46:06.993431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:06.993431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05616","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlf9ZoWs9a8cULLS3qJ1g7QcvLAWbChe0+heAaic7mzdDCMGPxJvGsVYONiJFpDglxzWwiGHUOpH73tRav5cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:22:45.366399Z"},"content_sha256":"2ced1db94aa8ace691932d57657408ecc2cc8db232a874d8bf22358171278721","schema_version":"1.0","event_id":"sha256:2ced1db94aa8ace691932d57657408ecc2cc8db232a874d8bf22358171278721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QB7B2J47OIPGXH564HKNIS3NF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mao Shinoda","submitted_at":"2017-04-19T05:23:54Z","abstract_excerpt":"Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given \"performance\" function. For a continuous self-map of a compact metric space and a dense set of continuous performance functions, we show that the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures which are fully supported and have positive entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05616","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7emp2Gs8H8YLnOUFN9dCOFjjpa2LjUBSuk71Nu/jhnlj6s41pMAJ133kHYRcTJNpZQvar9fdrcvSq4hxqlC3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:22:45.366745Z"},"content_sha256":"ede726b220e6f8dc4737807c97148fec31057528c08dd1b4f263382661e25815","schema_version":"1.0","event_id":"sha256:ede726b220e6f8dc4737807c97148fec31057528c08dd1b4f263382661e25815"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QB7B2J47OIPGXH564HKNIS3NF3/bundle.json","state_url":"https://pith.science/pith/QB7B2J47OIPGXH564HKNIS3NF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QB7B2J47OIPGXH564HKNIS3NF3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T11:22:45Z","links":{"resolver":"https://pith.science/pith/QB7B2J47OIPGXH564HKNIS3NF3","bundle":"https://pith.science/pith/QB7B2J47OIPGXH564HKNIS3NF3/bundle.json","state":"https://pith.science/pith/QB7B2J47OIPGXH564HKNIS3NF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QB7B2J47OIPGXH564HKNIS3NF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QB7B2J47OIPGXH564HKNIS3NF3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f07532d5798250b55c56a1985fcfd519d743d47da7a7bde0fc79bca71bb43ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-19T05:23:54Z","title_canon_sha256":"a3dbe345c27858ae1535df009dcc6d66c3178a21f17844c1f303a7f9e1e159c1"},"schema_version":"1.0","source":{"id":"1704.05616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05616","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05616v1","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05616","created_at":"2026-05-18T00:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"QB7B2J47OIPG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QB7B2J47OIPGXH56","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QB7B2J47","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:ede726b220e6f8dc4737807c97148fec31057528c08dd1b4f263382661e25815","target":"graph","created_at":"2026-05-18T00:46:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given \"performance\" function. For a continuous self-map of a compact metric space and a dense set of continuous performance functions, we show that the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures which are fully supported and have positive entropy.","authors_text":"Mao Shinoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-19T05:23:54Z","title":"Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05616","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2ced1db94aa8ace691932d57657408ecc2cc8db232a874d8bf22358171278721","target":"record","created_at":"2026-05-18T00:46:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f07532d5798250b55c56a1985fcfd519d743d47da7a7bde0fc79bca71bb43ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-19T05:23:54Z","title_canon_sha256":"a3dbe345c27858ae1535df009dcc6d66c3178a21f17844c1f303a7f9e1e159c1"},"schema_version":"1.0","source":{"id":"1704.05616","kind":"arxiv","version":1}},"canonical_sha256":"807e1d279f721e6b9fbee1d4d44b6d2ef5479b19d6a67ce802752dfba77cd2a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"807e1d279f721e6b9fbee1d4d44b6d2ef5479b19d6a67ce802752dfba77cd2a4","first_computed_at":"2026-05-18T00:46:06.993431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:06.993431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bicM/la4j+u+Lrc5rAeISlQx6wLCDuWdEpGjUQ/Vvc7bmd9LBclUMguoL22zAueQrFYDnhIgRVxu4DHhWcH4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:06.993810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ced1db94aa8ace691932d57657408ecc2cc8db232a874d8bf22358171278721","sha256:ede726b220e6f8dc4737807c97148fec31057528c08dd1b4f263382661e25815"],"state_sha256":"df41d04b0a1a605353784eb3f8b051b7684e75734fda616ea4ffd9b12152028c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9AU7Rj0EBVa6s5PGIKAYxpTdKSkS7hfN3IecG4/3+dIoj7a4YzPHBlva8ohBq5TLlHMNtC4HWf2k1XTbFSnSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:22:45.368697Z","bundle_sha256":"ed3e24288c5864f1b9bc4d1fad6215f3d5288cae252ea84cfac7c075c4e4464e"}}